### Abstract

We study dimensional reductions of noncommutative electrodynamics on flat space, which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenböck geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the non-commutativity scale. The effective field theory can also contain higher curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described. ©2001 The American Physical Society.

Original language | English |
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Article number | 104019 |

Journal | Physical Review D - Particles and Fields |

Volume | 64 |

Issue number | 10 |

Publication status | Published - 15 Nov 2001 |

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## Cite this

*Physical Review D - Particles and Fields*,

*64*(10), [104019].